Chapter 11

Solutions

Shaun Williams, PhD

The Composition of Solutions

A solution is:
- A homogeneous mixture with uniform composition throughout
- Composed of:
  - Solute
    - Substance being dissolved
    - Usually present in the lesser amount
  - Solvent
    - Substance doing the dissolving
    - Usually present in the greater amount

Making a Solution

A photograph showing table salt, sodium chloride, being poured into a beaker of water.

What is the solute?
What is the solvent?

Various Solutions

Photograph of adding sodium chloride solid to water, bubbling hydrogen chloride gas into water, and adding solid sodium hydroxide to water.

Solubility

How readily or completely a solute dissolves in a solvent
- A soluble ionic compound dissociates into ions when dissolved in water.
- Insoluble compounds remain mostly undissociated in their ionic, crystalline structure.
The solubilities for ionic compounds do not follow a predictable pattern
- Must be recalled from experimental data
- Solubility rules are listed on the next slide

Solubility Rules

#	Ions	Rules
1	\( \chem{Na^+,\, K^+,\, NH_4^+} \)	Most salts of sodium, potassium, and ammonium ions are soluble.
2	\( \chem{NO_3^-} \)	All nitrates are soluble.
3	\( \chem{SO_4^{2-}} \)	Most sulfates are soluble. Exceptions: \(\chem{BaSO_4}\), \(\chem{SrSO_4}\), \(\chem{PbSO_4}\), \(\chem{CaSO_4}\), \(\chem{Hg_2SO_4}\), & \(\chem{Ag_2SO_4}\)
4	\( \chem{Cl^-,\, Br^-,\, I^-} \)	Most chlorides, bromides, and iodides are soluble. Exceptions: \(\chem{AgX}\), \(\chem{Hg_2X}\), \(\chem{PbX_2}\), & \(\chem{HgI_2}\) (\(\chem{X = Cl,\, Br,\, or\, I)}\)
5	\( \chem{Ag^+} \)	Silver salts are insoluble.
6	\( \chem{O^{2-},\, OH^-} \)	Oxides and hydroxides are insoluble. Exceptions: \(\chem{Ba(OH)_2}\) & \(\chem{Ca(OH)_2}\) (somewhat soluble)
7	\( \chem{S^{2-}} \)	Sulfides are insoluble. Exceptions: Salts of alkaline metals and alkaline earth metal ions
8	\( \chem{CrO_4^{2-}} \)	Most chromates are insoluble. Exceptions: Salts of \(\chem{Mg^{2+}}\), \(\chem{Ca^{2+}}\), \(\chem{Al^{3+}}\), and \(\chem{Ni^{2+}}\)
9	\( \chem{CO_3^{2-},\, PO_4^{2-},\, SO_3^{2-},\, SiO_3^{2-}} \)	Most carbonates, phosphates, sulfites, and silicates are insoluble.

Electrolytes

A solution that conducts electricity
Two kinds of electrolytes:
- Strong electrolyte
  - A solute that dissociates completely into ions in aqueous solution
- Weak electrolyte
  - A solute that dissociates partially into ions in aqueous solution
- Nonelectrolyte
  - A solute that does not dissociate into ions in aqueous solution

Examples of Electrolytes

Adding nitric acid, sodium chloride, sodium hydroxide, or hydrochloric acid to water allows the solution to conduct electricity well.

Like Dissolves Like

When the bonding in a solvent is similar to the bonding in a solute, then the solute will dissolve in the solvent.
- Polar covalent solvents dissolve polar covalent solutes.
- Nonpolar covalent solvents dissolve nonpolar covalent solutes.
- See the table below

Solute	Solvent
Solute	Polar	Nonpolar
Ionic	Soluble	Insoluble
Polar	Soluble	Insoluble
Nonpolar	Insoluble	Soluble

The Solution Process

When table salt is added to water, the water pulls apart the sodium cations and the chloride anions.

Solution Process

Ion-dipole force
- An attraction between an ion and a polar molecule
When an ionic compound dissolves in water:
- Ionic bonds in the solute break.
- Hydrogen bonds between water molecules break.
- Ion-dipole forces form between ions and water molecules.

Images of a sodium cation surrounded by six water molecules pointing the negative end of their dipole at the ion and a chloride anion surrounded by six water molecules pointing the positive end of their dipoles are the anion.

The Energetics of the Solution Process

It takes every to break up the molecules of the solid and liquid and you get energy when they are then mixed.

Heat of Solution

The difference between the energy required for separation of solute and solvent and the energy released upon formation of ion-dipole interactions
When the solvation process provides more energy than is needed to separate the pure solvent and solvent particles, the heat of solution is negative, and the overall dissolving process is exothermic.

Endothermic Solution Process

It takes more energy to break up the solute and the solvent than you get out when the solute and solvent are mixed. Therefore the process is endothermic.

Solution Process for Nonpolar-Nonpolar Interactions

Purple crystals of solid iodine are mixed with clear liquid carbon tetrachloride to make a purple solution.

Entropy

A measure of the tendency for matter to become disordered or random in its distribution
Matter spontaneously changes from a state of order to a state of randomness, unless energy changes oppose it.
Solutions form because the makeup of the solution naturally tends toward disorganization.

Entropy in Dissolving

Pure water and crystalling table salt are quite order and therefore have low entropy. When the salt dissolves in the water, the solution has a very high entropy.

Factors that Affect Solubility

Three factors affect solubility:
- Structure
- Temperature
- Pressure

Carbon tetrachloride and hexane are both nonpolar so when they are poured together they dissolved into a solution.

Structure

For a solid to be soluble in a given solvent, the energy released by the solvation process must compensate for all of the energy required to break up the forces at work both within the solute and the solvent.
- Entropy is also a factor
The solubility (or miscibility) of liquids in other liquids depends largely on the polarity of the solute and solvent molecules.

Long polar molecules do not dissolved in water while small polar molecules do dissolve in water.

Temperature

Affects the solubility of most substances in water
- Most ionic solids are more soluble in water at higher temperatures
- Gases are less soluble as temperature increases

Plots showing that as the temperature of the solution increases, the amount of solids that can dissolve in the liquid increase while the amount of gases that can dissolve in the hotter liquid decreases.

Pressure

Affects gases but not liquids or solids
The solubility of a gas in a liquid is directly proportional to the pressure of the gas above the liquid
An increase in pressure results in an increase in solubility of a gas

Pressure Effect in Action

A cylinder contains a liquid and gas. When the piston is compressed, thereby conpressing the gas, the amount of the gas that can dissolve in the liquid increases.

Measuring Concentrations of Solutions

Concentration
- The relative amounts of the solutes and solvent that make up the solution \[ \text{Concentration} = \frac{\text{amount of solute}}{\text{amount of solution (or solvent)}} \]
Solubility
- The ratio that identifies the maximum amount of a solute that will dissolve in a particular solvent to form a stable solution under specified conditions
- A measure of maximum concentration
- Three types of concentrated solution:
  - Saturated solution
  - Unsaturated solution
  - Supersaturated solution

Saturated Solution

A solution that contains the maximum possible amount of solute
When this type of solution forms, a dynamic equilibrium is established.
Undissolved solute continues to dissolve, but at the same time, previously dissolved solute is deposited from solution.

A beaker containing a clear liquid and a yellow solid, lead(II) iodide.

Supersaturated Solution

A solution that contains more than the maximum possible amount of solute
Unsaturated solution
- A solution that contains less than the maximum possible amount of solute

A clear supersaturated solution has a small seed crystal dropped into this. This causes all of the excess solute to rapidly precipiate out of the solution.

Concentration Units

Unit	Definition
Percent by mass	\( \frac{\text{grams of solute}}{\text{grams of solution}} \times 100\% \)
Percent by volume	\( \frac{\text{volume of solute}}{\text{volume of solution}} \times 100\% \)
Mass/volume percent	\( \frac{\text{grams of solute}}{\text{volume of solution}} \times 100\% \)
Parts per million	\( \frac{\text{grams of solute}}{\text{grams of solution}} \times 10^6 \)
Parts per billion	\( \frac{\text{grams of solute}}{\text{grams of solution}} \times 10^9 \)
Molarity (\( M\))	\( \frac{\text{moles of solute}}{\text{liters of solution}} \)
Molality (\( m \))	\( \frac{\text{moles of solute}}{\text{kilograms of solvent}} \)

Percent by Mass

Is calculated by dividing the solute mass by the mass of the solution and multiplying it by 100% \[ \text{Percent by mass} = \frac{\text{mass (solute)}}{\text{mass (solution)}} \times 100\% \]
To find the mass of the solution, we can add the mass of the solute to the mass of the solvent.

Percent by Volume

Is calculated by dividing the solute volume by the solution volume and multiplying by 100% \[ \text{Percent by volume} = \frac{\text{volume (solute)}}{\text{volume (solution)}} \times 100\% \]
The volume of the solution must be measured. Volumes are not additive like masses.

Mass/Volume Percent

Is calculated by dividing the solute mass by the volume of solution and multiplying by 100% \[ \text{Mass/Volume Percent} = \frac{\text{grams (solute)}}{\text{volume (solution)}} \times 100\% \]
Example:
- The concentration of NaCl in a saline bag is 0.9%. Therefore, for every 100 mL of solution, the mass of NaCl present is 0.9 g.

Parts per Million and Billion

Parts per million
- Is calculated by dividing the mass of solute by the mass of solution and multiplying by 1 million (\(10^6\)) \[ \text{Parts per million} = \frac{\text{mass (solute)}}{\text{mass (solution)}} \times 10^6 \]
Parts per billion
- Is calculated by dividing the mass of solute by the mass of solution and multiplying by 1 billion (\(10^9\)) \[ \text{Parts per billion} = \frac{\text{mass (solute)}}{\text{mass (solution)}} \times 10^9 \]

Molarity

The ratio of moles of solute to the volume of solution in liters \[ \text{Molarity}(M) = \frac{\text{moles (solute)}}{\text{liters (solution)}} \]
Example:
- A solution contains 117 g of potassium hydroxide (KOH) dissolved in sufficient water to give a total volume of 2.00 L. The molar mass of KOH is 56.11 g/mol. What is the molarity of the aqueous potassium hydroxide solution?

Molality

If the temperature of a solution increases, the molarity of the solution changes because the volume changes.
Molality does not change with temperature because it divides moles of solute with the mass of solution. \[ \text{Molality}(m) = \frac{\text{moles (solute)}}{\text{kg (solvent)}} \]

Quantities for Reactions That Occur in Aqueous Solution

Precipitation Reactions

The cation from one reactant combines with the anion from another reactant to form an insoluble compound, called a precipitate.
Example
- When a solution of lead(II) nitrate is mixed with a solution of potassium chromate, a yellow precipitate forms according to the equation: \[ \chem{Pb(NO_3)_2(aq) + K_2CrO_4(aq) \rightarrow 2 KNO_3(aq) + PbCrO_4(s)} \] What volume of 0.105 M lead(II) nitrate is required to react with 100.0 mL of 0.120 M potassium chromate? What mass of \(\chem{PbCrO_4}\) solid forms?

Acid-Base Titrations

Titration
- The process of determining the concentration of one substance in solution by reacting it with a solution of another substance that has a known concentration
Equivalence point
- The point in a titration at which the moles of the acid equal the moles of the base
End point
- The point in a titration where the indicator changes color
- Slightly different than the equivalence point, but a good estimation

Acid-Base Titration Observation

When a clear acid is added to a clear base, nothing changes even though the reaction is occuring. The addition of the indicator cause the color to change from clear to purple when the moles of acid and moles of base are equal.

Colligative Properties

A property that does not depend on the identity of a solute in solution
Vary only with the number of solute particles present in a specific quantity of solvent
4 colligative properties:
- Osmotic pressure
- Vapor pressure lowering
- Boiling point elevation
- Freezing point depression

Osmotic Pressure

Osmosis
- A process in which solvent molecules diffuse through a barrier that does not allow the passage of solute particles
The barrier is called a semipermeable membrane.
- A membrane that allows the passage of some substances but not others
Osmotic Pressure
- Pressure that can be exerted on the solution to prevent osmosis

A membrane with holes seperating an aqueous solution from pure water. Water flows from the pure water side to the solution side.

Measuring Osmotic Pressure

A semipermeable membrane at the bottom of a glass tube bent into a U shape. Osmosis forces one toward the solution side thereby making the water level higher on that side.

Vapor Pressure Lowering

Solutes come in 2 forms:
- Volatile - Solutes that readily form a gas
- Nonvolatile - Solutes that DO NOT readily form a gas
Generally, the addition of a solute lowers the vapor pressure of a solution when compared to the pure solvent.

Sealed containers of pure water and a solution of a nonvolatile solute. The amount of water vapor above the pure water is higher than the amount of water vapor above the pure water.

Effect of Vapor Pressure Lowering

Two beakers, one with pure water and the other a sugar solution, are placed in a sealed container. Over time, the volume of pure water drops while the volume of the sugar solution increases.

Phase Diagram

A plot of pressure versus temperature for water showing the regions where solid, liquid, and gases exist. When a solute is added, the triple point is reduced thereby shifting the melting line to lower temperatures and shifting the boiling line to higher temperatures.

Boiling Point Elevation

The addition of solute affects the boiling point because it affects the vapor pressure.
The boiling point is raised with the addition of solute in comparison to the pure solvent.
An equation that gives the increase in boiling point: \[ \Delta T_b = K_b m \] where \( \Delta T_b \) is the increase in temperature from the pure solvent's boiling point, \( K_b \) is the boiling point constant, which is characteristic of a particular solvent, and \( m \) is the molality (moles of solute per kg of solution)

Freezing Point Depression

The freezing point is lowered with the addition of solute in comparison to the pure solvent.
An equation that gives the decrease in freezing point: \[ \Delta T_f = K_f m \] where \( \Delta T_f \) is the decrease in temperature from the pure solvent's freezing point, \( K_f \) is the freezing point constant, which is characteristic of a particular solvent, and \( m \) is the molality (moles of solute per kg of solution)

Chapter 11 Solutions